UG-BNAN-276-Written-Assignment-Chapter-6 Charles Copeland

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Statistical Inference in Management Week 4: Written Assignment Chapter 6 Charles Copeland Written Assignment Chapter 6 1. What are the two types of questions that we will attempt to find the answers for in this chapter? - "What is the outcome when given a probability?" - “ What is the probability of an outcome happening?" 2. What information do you need to have when solving problems about a Uniform distribution? What about a Normal distribution? - The lower and upper boundaries. - Means and standard deviations. 3. Which distribution is associated with a z-score? - Normal Distribution Which distribution (normal or uniform) has outcomes having an unequal probability of occurring? - Normal Distribution Which has all outcomes with an equal probability of occurring? - Uniform What do the shapes of the normal and uniform distributions look like? Why does the uniform have the shape that it does? - Normal is bell-shaped, whereas uniform is rectangular, indicating that each result has an equal chance of occurring. Which distribution has bounds? Which does not? - Uniform has bounds, Normal doesn’t. 4. What is the probability that a perfectly functioning clock is at the 35 th minute of any respective hour? What type of distribution would this be? - The likelihood of a perfectly working clock being at the 35th minute of any given hour is 1/35. A uniform distribution is what would be used. 5. Why is the roll of a dice a discrete uniform distribution? - There are not an endless number of outcomes between two distinct numbers of dice; for example, there are not an infinite number of numbers that may be rolled between 2 and 3. 6. In words, what is the formula for height of a uniform distribution? - 1/(b-a) 7. Assume you are on your own private Wi-Fi network and the time it takes to load your D2L home page is between 0 to 1000 milliseconds (msc). Thus, it would be described as a continuous Uniform distribution. Calculate the probability that the previously mentioned D2L home page will load in the next 300 milliseconds.

Page 2 of 4 Copyright © Arizona Board of Regents - The likelihood of the D2L home page loading in the next 300 milliseconds is 0.30. 8. What is the percent of observations that have heights between (and including) 4.9 and 5.1 feet? - The percentage of observations with heights between (and including) 4.9 and 5.1 feet is 23.1%. 9. What are the three different outcomes that we can ask questions about when it concerns a continuous distribution? - The probability of a result being smaller than a particular quantity. - The probability that a result will be larger than a specified quantity. - Probability that a result falls between particular quantities. 10. Write the argument (in terms of a Random Variable) for the probability of the shaded region below. - To calculate the probability of the shaded region below the random variable Z, we must first define the variable and its probability distribution. The likelihood of a shaded area is P = P (X > x) 11. Write the argument (in terms of a Random Variable) for the probability of the shaded region below.

Page 3 of 4 Copyright © Arizona Board of Regents - P (a < x < b) 12. Write the argument (in terms of a Random Variable) for the probability of the shaded region below. - P (X < x) 13. What type of transformation (x to z to p) is shown below? - Standard Transformation. Write the argument for the probability of the outcome you are trying to solve for. - P (X < x). 14. If months-to-market for an IoT product follows a normal distribution, what is the probability that a company’s batch of latest products will take less than 6 months on average? It is known that past average time is 4.2 months with a standard deviation of 1.2 months. - 0.9332 15. What is the probability that Under Armour will surpass $13.3B in sales this year if the expected return is $15B with a standard deviation of $2.2B? Assume a normal distribution for yearly sales. - 0.7799 16. Wins for NFL teams are normally distributed. What is the probability that the NFL’s Green Bay Packers will win between 9 to 11 games if the expected win total is 10.2 with a standard deviation of 1.0? - 0.0968

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Page 4 of 4 Copyright © Arizona Board of Regents 17. Assuming the yearly historical sales volume of Apple’s iPhone XI is normally distributed with a mean of 52M phones and standard deviation of 5M. How many iPhone XI’s should Apple order so that it meets at least 93% of customer demand? - There should be at least 60M apple iPhone orders to meet up 93% demand of customer demand.

UG-BNAN-276-Written-Assignment-Chapter-6 Charles Copeland

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